(x-4/x+1)/(x-3/x-1)

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Solution for (x-4/x+1)/(x-3/x-1) equation: 


D( x )

x-(3/x)-1 = 0

x = 0

x-(3/x)-1 = 0

x-(3/x)-1 = 0

x-3*x^-1-1 = 0

1*x^1-3*x^-1-1*x^0 = 0

(1*x^2-1*x^1-3*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-1*x^1-3*x^0) = 0

x^1

x^2-x-3 = 0

x^2-x-3 = 0

DELTA = (-1)^2-(-3*1*4)

DELTA = 13

DELTA > 0

x = (13^(1/2)+1)/(1*2) or x = (1-13^(1/2))/(1*2)

x = (13^(1/2)+1)/2 or x = (1-13^(1/2))/2

x in { (1-13^(1/2))/2, (13^(1/2)+1)/2} 

x = 0

x = 0

x in (-oo:(1-13^(1/2))/2) U ((1-13^(1/2))/2:0) U (0:(13^(1/2)+1)/2) U ((13^(1/2)+1)/2:+oo)

(x-(4/x)+1)/(x-(3/x)-1) = 0

(x-4*x^-1+1)/(x-3*x^-1-1) = 0

x-4*x^-1+1 = 0

1*x^1-4*x^-1+1*x^0 = 0

(1*x^2+1*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2+1*x^1-4*x^0) = 0

x^1

x^2+x-4 = 0

x^2+x-4 = 0

DELTA = 1^2-(-4*1*4)

DELTA = 17

DELTA > 0

x = (17^(1/2)-1)/(1*2) or x = (-17^(1/2)-1)/(1*2)

x = (17^(1/2)-1)/2 or x = (-(17^(1/2)+1))/2

x in { (-(17^(1/2)+1))/2, (17^(1/2)-1)/2} 

(x+(17^(1/2)+1)/2)*(x-((17^(1/2)-1)/2)) = 0

x-3*x^-1-1 = 0

1*x^1-3*x^-1-1*x^0 = 0

(1*x^2-1*x^1-3*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-1*x^1-3*x^0) = 0

x^1

x^2-x-3 = 0

x^2-x-3 = 0

DELTA = (-1)^2-(-3*1*4)

DELTA = 13

DELTA > 0

x = (13^(1/2)+1)/(1*2) or x = (1-13^(1/2))/(1*2)

x = (13^(1/2)+1)/2 or x = (1-13^(1/2))/2

x in { (1-13^(1/2))/2, (13^(1/2)+1)/2} 

(x-((1-13^(1/2))/2))*(x-((13^(1/2)+1)/2)) = 0

((x+(17^(1/2)+1)/2)*(x-((17^(1/2)-1)/2)))/((x-((1-13^(1/2))/2))*(x-((13^(1/2)+1)/2))) = 0

( x+(17^(1/2)+1)/2 )

x+(17^(1/2)+1)/2 = 0 // - (17^(1/2)+1)/2

x = -((17^(1/2)+1)/2)

( x-((17^(1/2)-1)/2) )

x-((17^(1/2)-1)/2) = 0 // + (17^(1/2)-1)/2

x = (17^(1/2)-1)/2

x in { -((17^(1/2)+1)/2), (17^(1/2)-1)/2 }

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